• Frontmatter,
• Contents,
• 0. Introduction,
• 1. Topology of Representation Spaces,
• 2. Definition of ¿,
• 3. Various Properties of ¿,
• 4. The Dehn Surgery Formula,
• 5. Combinatorial Definition of ¿,
• 6. Consequences of the Dehn Surgery Formula,
• A. Dedekind Sums,
• B. Alexander Polynomials,
• Bibliography,

This book describes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case. Let R(X) denote the space of conjugacy classes of representations of p(X) into SU(2). Let (W,W,F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is declared to be an appropriately defined intersection number of R(W) and R(W) inside R(F). The definition of this intersection number is a delicate task, as the spaces involved have singularities.
A formula describing how l transforms under Dehn surgery is proved. The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of l. It is also shown that when M is a Z-homology sphere, l(M) determines the Rochlin invariant of M.